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Essential 3D Geometry: Unraveling the Mathematical Wonders Bernardo Camou, John Olive, Margarita Colucci, Graciela Garcia

Essential 3D Geometry

Unraveling the Mathematical Wonders

By Bernardo Camou, John Olive, Margarita Colucci and Graciela Garcia

Paperback ISBN: 978-1-60927-389-7, 114 pages


We live out our lives in a three dimensional world. However, our understanding of what this means is meager, and the study of 3D Geometry is markedly absent from our educational system. Essential 3D Geometry: Unraveling the Mathematical Wonders bridges the gap between current mathematical knowledge and our fascinating—and unexplored—3D world.

Originally developed by and for high school students, the material in Essential 3D Geometry has been successfully developed into a college-level text for pre-service teachers.

The book offers an original and unique approach for learning mathematics—iMAT engineering—which is based on the principle that learning mathematics is an integrated activity calling for multi-type presentations of mathematical objects through the use of different technologies.

The text begins with a thorough study of the building blocks of spatial structures, the five Platonic Solids. The material integrates 2D and 3D geometry, as well as algebra and trigonometry. Subsequent chapters cover a variety of topics including Thales' Theorem, the volume of the Platonic solids and non-regular tetrahedrons, circumcircles and circum-spheres, Archimedean Bodies, and spatial transformations.

Students will learn to produce and make use of three types of representation of 3D objects: solids or lattice models, Cabri 3D or GSP files, and constructions using a straight-edge and compass or free hand drawings. Representations will be developed using paper and pencil, craft technology, and computer technology. Beginning with simple activities like constructing concrete models, the material then moves on to abstract representations, reasoning, and exact calculations of surface areas and volumes.

Essential 3D Geometry is an excellent tool for introducing math educators to the concepts of 3D geometry, helping them go on to develop similar courses for their own students.

Teaching Resources

Adopting instructors will receive a complete set teaching resources, including Cabri 3D v2 and GSP v5 files of all of the figures and constructions for each chapter and sample exams. Contact a University Readers representative to request a sample.
Bernardo Camou has 20 years of experience teaching mathematics in secondary education. In 2004 he earned his Master of Didactics of Math at Grenoble University in France, the birthplace of the dynamic geometry software CABRI. After returning to his native country of Uruguay, he became the president of SEMUR, the National Association of Math Teachers. In 2009, he began work on his Ph.D. in mathematics education at the University of Georgia, graduating in May 2012. His dissertation topic, and his passion, is to help others discover the wonders of 3D Geometry.
Graciela García studied economics at the Universidad de la Republica for two years before going on to earn the title of Math Teacher at the Instituto de Profesores Artigas. She currently teaches at the Woodlands School, after having spent 37 years teaching math in public high schools. In addition to her work in mathematics education, Ms. Garcia studied social psychology at the Institution Pichon Riviere.
Dr. John Olive is Professor Emeritus of Mathematics Education at the University of Georgia. For over 30 years his research has focused on students’ mathematical thinking, and the development and use of technological tools to support that thinking. Dr. Olive has published over 30 papers, articles, monographs, and book chapters. He is also the co-author (with Dr. Leslie P. Steffe) of Children’s Fractional Knowledge, the culmination of 20 years of research into children’s constructions of fractions.

Dr. Olive was a member of the organizing committee for the ICMI Study 17 on Technology and was lead author of the chapter on learning in the study volume Technology Revisited: Rethinking the Terrain. He is currently on the editorial board for Springer’s book series on Mathematics Education in the Digital Era. He was Co-PI for the NSF supported project: Coordinating Students’ and Teachers’ Algebraic Reasoning (CoSTAR), and is currently directing the evaluation for Introducing Dynamic Number, a National Science Foundation-funded research and development project for KCP Technologies.
Maria Margarita Colucci earned the title of Math Teacher at the Instituto de Profesores Artigas (IPA) in Montevideo, Uruguay. For the past fifteen years she has been a high school math teacher at the Liceo N 15, as well as teaching at the Woodlands School where she is also coordinator of M.I.P. In addition to her work in math education, Ms. Colucci is involved in teacher education at the Instituto de Profesores Artigas in Montevideo, and the Centro Regional de Profesores in Maldonado. Her love for mathematics is linked to her wish to learn, to share her time, and to give others answers to the questions that carry our existence. She currently lives in Stockholm, Sweden.